Waveguide attenuator



States of New York Filed Dec. 24, 1959, Ser. No. 861,926

4 Claims. ((11. 333-'24) This invention relates to electromagnetic wave transmission systems and more particularly to transmission structures having nonreciprocal attenuation properties for use in such systems.

The use of materials having gyromagnetic properties to obtain both reciprocal and nonreciprocal effects in microwave transmission circuits is widely known and has found numerous and varied applications in electromagnetic wave systems of both the waveguide and the transmission line type.

Included among the new transmission components that have found widespread use in the microwave art is the so-cal-led isolator. The isolator may be defined as a circuit element which transmits without substantial loss electromagnetic waves propagating therethrough in one direction, designated the forward direction, whereas electromagnetic waves propagating in the opposite, or reverse, direction are attenuated by the isolator to the extent required by the system.

One particular class of isolator makes use of the resonance effect characteristic of all gyromagnetic materials. A typical isolator of this type comprises a vane of resonantly biased gyromagnetic material, asymmetrically located in the electromagnetic wave path. One of the char- Unite acteristics of such isolators is that the amount of attenuation that can be realized in the reverse or lossy direction is a function of the volume of the gy-romagnetic element. The greater the required attenuation, the greater must be the volume of gyromagnetic materialused. This basic requirement tends to make such isolators large, thus preeluding their use in systems in which small size is an essential requirement. Furthermore, the need for a large volume of gyromagnetic material complicates the biasing problem, making it difiicult to obtain a uniform biasing field throughout the gyromagnetic element. In addition, the use of a large voltune of material tends to increase the losses in the forward, or low-loss direction of propagation and to substantially increase the permittivity of the wave path. 7 It is, therefore, an object of this invention to introduce a high order of nonreciprocal attenuation in electromagnetic wave systems using small samples of resonantly biased gyromagnetic material.

Recognizing that a small sample of resonantly biased gyromagnetic material behaves as a rotating point magnetic dipole, which is energized by the incident microwave field, it is proposed to utilize the reradiated microwave energy produced by such a magnetic dipole to cancel the incident field. Accordingly, a sample of gyromagnetic material is placed in a region of a wave path wherein the high frequency magnetic field component is circularly polarized. In one direction of propagation, for which the direction of rotation of'the high frequency magnetic field is compatible with the natural precessional direction of the sample, the gyromagnetic material is strongly coupled to the incident field, and the induced dipole reradiates in the same direction as the incident wave only. In particular, at resonance, the reradiated wave is 180 degrees out 3,M@,Z76 Patented June 19, 1962 ice capable of completely absorbing the incident wave in an extremely small sample of gyromagnetic material. Because the diameter of the sample is of the order of only 25 to mils, losses on the forward direction are correspondingly small. Thus, isolators constructed in accordance with the invention have very high reverse-to-forward loss ratios.

These and other objects and advantages, the nature of the present invention, and its various features, will appear more fully upon consideration of the various illustrative embodiments now to be described in detail in connection with the accompanying drawings, in which:

FIG. 1 shows an isolator in accordance with the invention;

FIG. 2 shows, by way of. illustration, the equivalent circuit of the embodiment of FIG. 1; and

FIG. 3 is a second embodiment of the invention.

Referring more specifically to FIG. 1, an isolator is shown as an illustrative embodiment of the present invention. The isolator comprises a section 11 of bounded electrical transmission line for guiding wave energy which maybe a rectangular waveguide of the metallic shield type having a wide internal cross-sectional dimension a of at least one-half wavelength of the wave energy to be propagated therethrough and a narrow dimension b substantially one-half of the wide dimension.

Located midway between the wide walls and at a distance d from one of the narrow walls is a small sphere 12 of gyromagnetic material suitably supported by means of a slab 13 of low-loss dielectric material. The term gyromagnetic materia is employed here in its accepted sense as designating the class of magnetically polarizable materials having unpaired spin systems involving portions of the atoms thereof that are capable of being aligned by yttrium-iron garnet.

of phase with the incident wave and tends to cancel it.

Fora specific size sample, the reradiated field is such as to completely cancel the incident field with substantially all I the power contained in the wave being absorbed in the sample.

An isolator, in accordance with the invention, is thus Element l2 is biased by a steady magnetic field H normal to the direction of propagation of wave energy along the waveguide. This field may be supplied by an electric solenoid, by a permanent magnet structure, or element 12 may itself be permanently magnetized, if desired.

The problem of'radiation damping produced by mag- I netic resonance effects has been treated by S. Bloom (Journal of Applied Physics 28, 1957, page 800) and by N. Bloembergen and R. V. Pound (Physical Review 95, 1954, page 8). They, however, have considered the spin system in the gyromagnetic element when coupled to a lumped resonant circuit containing damping. While these treatments are adequate where the magnetization is coupled to a cavity or resonantt circuit, the nonreciprocal properties found in waveguides are not evident, and a solution to the more general boundary-valueproblem is more appropriate. 1

For reference purposes, guide 11 and element 12 are located in a coordinate system represented by the mutually perpendicular vectors 14 labeled x, y and z. Vector x indicates a positive sense along the wide transverse dimension of guide 11. The y vector indicates a positive sense along thenarrow transverse dimension of guide 11,- whereas the z vector indicates a positive sense along the longitudinal direction of the guide, parallel to the direc- A wave moving in the +z direction has components 7123 H m sin 4 nu-r1) Sin E imrz) [.L is the permeability of the wave path, 6 is the permittivity of the Wave path, H is the amplitude of 'H in the center of the Waveguide, A is the wavelength of the electromagnetic wave in the unbounded dielectric 13 and is equal to t is the free space wavelength of the electromagnetic wave, w is 211- times the frequency of the electromagnetic wave,

where and I is the propagation constant along the guide.

-It is convenient to think of the magnetic field as the superposition of clockwise and counterclockwise rotating components as seen looking on the x=z plane from y=oo. These components may be expressed as If I ei (mt-Ta) 2 cos (p m H m sin p) (wt-Ta) Hm 2 cos (p e In these equations the substitutions h A 2 i sin cos /1 (3) have been made.

For a sample placed in the x=z plane at x=d width H in the +y direction, the counterclockwise component is the component and'produces a transverse magnetic dipole moment m, which at resonance is Where v is the volume of the sample and (X-K) is the loss component of the susceptibility of a gyromagnetic substance under the influence of a circularly polarized magnetic field. Here an effective magnetic field, H is used rather than H to take into account the reaction of m on the fields within the Waveguide. For the time being we shall write Hm: 2 cos 0 and the proportionality factor K will be. obtained pres ently.

a t The general expressions for the far fields radiated by a rotating magnetic dipole in a waveguide are given as:

vrx mi 21112 sinsin --o E i(wi7-Iz) Ey i s a b sin 24b 6 vrm sin 1} sin -w) Hx= a a cum-r5) (6) 0% sin (,0 11-50 1rd j'lrm cos sin a a mit-m 11% cos forv radiation in the +2 direction, and

21m sin L96 sin -l-ga) n fi i(..t+r.

e a b sin 2e 1rm cos L7: sin -l-rp) I j(wt+Iz) (l) 4 (1% sin (p jn-m cos E sin -i-ga) H i (mt+Iz) 11% cos 40 for radiation in the -z direction.

The counterclockwise or component of the exciting magnetic field leads in by 1r/ 2; therefore the radiated fields in the +z direction are out of phase with the incident Waves. The voltage transmission coefficient is unity plus the ratio of a component of the Wave reradiated in the +z direction to the analogous component of the incident wave in'the +2 direction. From the components given by Equations 1 and 6, the transmission coefiicient is lam 5w T 1 8 (1% sin 2 p Similarly, the reflection coefficient is Maw) an a. gut R a b sin 2 In (8) and (9) in has been eliminated with the use of (4) and (5). The power-absorbed by the magnetization at resonance is v a= etf which becomes 2 -2 1. P 27rK /L U()( A. )H., Sin (a go (11) e 4 cos e The power flow for the incident Wave is (lb 1. H 02 12 V 4 6 cos p so that the power absorption coefiicient is K 21rv(x"-K) Sill go) A= T (1% sin 2gp (13) v I 2a b Note that F is independent of frequency insofar as K") is frequency independent. Its significance will become apparent shortly.

The transmission, reflection and absorption coefficients now become Let us now consider several situations. It is seen from Equation 18 that the reflection coefficient is the same for positions equidistant from the center of the waveguide, and becomes zero when a 1r p These distances correspond to the two positions of circular polarization within the guide, as is evident from Equation 2. For 1rd/a however, resonance is not excited in the gyromagnetic material. In the other position, for which and resonance is strongly excited. Since, from EquationlS, 12:0 in this position, the dipole can only radiate in the forward direction. The transmission coefficient for.

The minimum value of F for which all the incident power can be transferred to the sample is unity. From Equation 3 the frequency at which this occurs is V times the cutoff frequency. For single crystal material for which "K=41rM /AH, where AH is the intrinsic half-width at half power, this is possible only when 1r?) 41l'M 5 3 AH 21 (23) The scattering matrix shows the nonreciprocal nature of the system. s: 1

(1-cos cos 2 1+F sin 2p sin 2 4 21rd 27rd cos 2-cos l-l-F sin F a sin 2,0

. 6 Since the diagonal elements are identical, the reflection coefficient from either end of the waveguide is the same for a given sample position. When the sample is in the center of the guide or on either wall, the off-diagonal e ements are identical and the device is reciprocal. For all other positions the system is nonreciprocal.

At the position of pure circular polarization a useful equivalent circuit is a three-arm circulator with a resonant cavity on one arm as shown in FIG. 2. The quarter wave section in arm 2 provides proper phasing at the output. From Equation 16 it is seen that for a given size guide F is a function of the volume of the sample and its susceptibility at resonance. In terms of the equivalent circuit, the device acts as an isolator when the cavity is critically coupled to the transmission line connected. to arm 2 of the circulator. Under this condition, power at the resonant frequency entering arm 1 is completely absorbed in the cavity. However, power entering arm 3 leaves by way of arm 1 unattenuated. Critical coupling is obtained by'adjusting the volumeof the gyromagnetic sample in accordance with the equation F sin -2=l.

When the cavity in the equivalent circuit is overc'oupled, that is, F sin 2 l, a portion of the power entering arm 1 will be reflected at the cavity and will leave by way of arm 3. The remaining portion of the incident energy will be absorbed in the cavity. At resonance there will be a differential phase shift of 180 degrees for wave energy propagating from 1 to 3 as compared to wave energy propagating from 3 to l.

Near resonance, but not exactly at rmonance, the differential phase shift will deviate from degrees in the manner typical of a simple tuned circuit.

In the embodiment of FIG. 1 the gyromagnetic element 12 is shown as a sphere. It is to be understood, however, that this element may have any other convenient physical configuration without adversely affecting the operation of the invention. Whatis important, however, is that the volume of element 12 satisfy the conditions set forth in Equation 22 and that the dimensions of the sample in the plane of the radio frequency magnetic field be small compared to a wavelength.

In a second embodiment of the invention, shown in FIG. 3, circular cylindrical waveguide is utilized. The isolator comprises a section 36 of cylindrical wave guide of radius R, proportioned to support wave energy in the 'IE mode of propagation.

A portion of the electrical field configuration is also shown in FIG. 3. The electric field pattern for the TE mode is transverse to the guide axis 34 and is indicated, for the left-hand side of guide 30, by the vectors 35. The field pattern for the right-hand side is essentially the mirror image of the left-hand side. The center vector E, passing through the guide axis 34, defines the direction of polarization of the wave and is referred to as the principal electric field vector.

Located a distance p from the guide axis 34-, along a radius normal to the principal vector E, is a small sphere 31 of gyromagnetic material, suitably supported by means of a disk of low-loss dielectric material 32.

Element 31 is biased by means of a steady magnetic field H directed normal to the direction of wave propagation along the waveguide and parallel to the direction of the principal vector E.

Applying the same analytical technique as was applied to the embodiment of FIG. 1, it can 'be shown that complete absorption is obtainedin the reverse direction when where v is the volume of gyromagnetic material;

p is the radial distance of the gyromagnetic material from the guide axis;

A is the guide wavelength of the electromagnetic wave for the TE mode;

J is Bessels function of the first kind and first order;

I is the first derivativeof Bessels function;

R is the guide radius;

( "K") is the susceptibility at resonance of the gyromagnetic material; and

k is the constant 1.8412, such that J' (k' )=0.

In all cases it is understood that the abovedescribed arrangements are illustrative of a small number of the many possible specific embodiments which can represent applications of the principles of the invention. Numerous and varied other arrangements can readily be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention.

What is claimed is:

1. In an electromagnetic wave transmission system supportive of dominant mode wave energy at a given frequency, an attenuator comprising a rectangular waveguide having a wide transverse dimension a and a narrow transverse direction b, an element of gyromagne-tic material having a volume v and susceptibility K) at resonance disposed Within said guide at a distance d along said wide dimension where the volume of said element and said location within said guide are related by a (w x a M) X K 8 where AH is the intrinsic half line width at half power of said element and M is the saturation magnetization of said element. 7 3. The combination according to claim 1 wherein said gyromagnetic material is located in a region of circular polarization for which where is the free space Wavelength at said given frequency.

4. An electromagnetic wave transmission path supportive of Wave energy in the TE mode at a given frequency, an isolator comprising a circular cylindrical Wave guide of radius R, an element of gyrornagnetic material having a volume v and a susceptibility "1 at resonance disposed Within said guide a distance p from the guide aXis, where the volume of said element and said location within said guide are related by is the guide Wavelength of said Wave energy;

1 is the Bessel function of the first kind and order; 1' is the first derivation of said Bessel function; and it' is a. constant equal to 1.8412, 7

and means for magnetically biasing said element to gyromagnetic resonance at said given frequency.

References Cited in the file of this patent UNITED STATES PATENTS 2,810,882 Walker Oct. 22, 1957 2,883,629 Suhl Apr. 21, 1959 2,922,125 Suhl Ian. 19, 1960 

